1. Field of the Invention
The present invention relates to an X-ray CT apparatus for reconstructing tomographic images, by utilizing projection data.
2. Related Background Art
As illustrated in FIG. 4, in an X-ray CT (Computer Tomography) apparatus, an X-ray source 1 and an X-ray detector 2 are arranged so as to face each other, with a subject S being interposed between them; while the X-ray source 1 and the X-ray detector 2 or the subject S is are being revolved around a point within the subject S, each X-ray sequentially radiated by the X-ray source 1 is detected by the X-ray detector 2. By reconstructing and processing projection data created in this way, a tomographic image can be obtained. In this situation, the line that connects the X-ray source 1 with the center of the X-ray detector 2, i.e., the coordinate origin O for the projection data always passes through the revolution center point A.
However, if, due to mechanical misalignment, movement of the subject S, and the like, the line and the revolution center point A of the subject S deviate from each other, i.e. a condition changes from a state as illustrated in FIG. 5A to a state as illustrated in FIG. 5B, the coordinate origin of the projection data for the subject S is shifted. In FIGS. 5A and 5B, the case where the subject S rotates is illustrated; however, also in the case where the subject S is fixed, and where the X-ray source 1 and the X-ray detector revolve, the coordinate origin of the projection data for the subject S is shifted.
If the projection data whose coordinate system has been shifted in such a way is considered as if not shifted and is reconstructed as it is, an artifact or significant deterioration in an image may be caused. In order to detect such a position deviation of the revolution center point, for example, as disclosed in Japanese Patent Application Laid-Open No. 2002-336237, by taking images of a calibration phantom or a marker, the detection of a position deviation has conventionally been implemented.
However, when the position deviation of the revolution center point is detected by utilizing a calibration phantom, it is necessary to newly create a calibration phantom, and, further, it takes a time to collect data, while taking images of the phantom, whereby the efficiency is lowered. In addition, when a marker is used, it is necessary to newly create a marker; because the marker appears in a reconstructed tomographic image, diagnosis is hindered.
In the case where a fan beam is used as the X-ray source 1, as illustrated in FIG. 6, the X-ray transmission path with a fan angle α coincides with the X-ray transmission path with a fan angle −α and with a projection angle being turned by 180°+2α. It means that, supposing that the transmission data value of a transmission path with a fan angle α and a projection angle β is g(α, β), the transmission data value g(−α, β+π+2α) of the opposite transmission path coincides with g(α, β). That is to say, Equation (1) is yielded.g(α,β)=g(−α,β+π+2α)  (1)
Equation (1) is rendered as in FIG. 7, on a sinogram.
In contrast, in the case where the revolution center point A of the subject S is deviated, as described above, the deviation appears as a shift of projection data in the coordinate system; thus, the deviation is rendered as in FIG. 8, on a sinogram, and is expressed by Equation (2).g(α,β)=g(−α+2x,β+π+2(α−x))  (2)
As described above, data that originally coincide appear on a sinogram, as expressed by Equation (1); however, in the case where a position deviation of the revolution center point A exists, data appear, as expressed by Equation (2).